THERMODYNAMICS Course No: ME 209 Department: Mechanical - PowerPoint PPT Presentation

Slide 1/18 THERMODYNAMICS Course No: ME 209 Department: Mechanical Engineering Instructor: U. N. Gaitonde Lecture 23: Open Thermodynamic Systems ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 2/18 Lecture 23: Open Thermodynamic Systems • Illustrations of open thermodynamic systems • A specific case for study and derivation • Generalisation • Application to typical engineering systems • Numerical Exercises ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 3/18 Illustrations • Turbines, compressors, pumps • Fans • Boilers, condensers, heat exchangers • Ducts • Rooms and buildings • Car • Human being • . . . . An open system is also known as a control volume (CV). ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 4/18 A schematic open system The inflows and outflows could be through ducts or through ports. The flows could also be continuously distributed along the boundary. ˙ m e 1 � V ˙ m e 2 ˙ m i 2 ˙ m e 3 ˙ m i 1 ˙ ˙ ˙ ˙ W S W S Q Q ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 5/18 A schematic open system (contd) e ˙ Q CV i ˙ W S It has 1 inlet and 1 outlet. ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 6/18 The Situation The control volume state: volume V ( t ) , Mass M ( t ) , Energy E ( t ) , Entropy S ( t ) etc.. The fluids at inlet (i) and exit (e) are in local equilibrium. The situation at inlet and exit is 1-dimensional (1D), with everything uniform across the cross-section. Inlet state: area A i , density ρ i , volume v i , energy e i , velocity V i , etc.; V i normal to A i . Exit state: area A e , density ρ e , volume v e , energy e e , velocity V e , etc.; V e normal to A e . ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 7/18 The Situation (contd) The rate of heat transfer to the CV from its surroundings is ˙ Q ( t ) . The rate at which work is done by the CV is ˙ W S ( t ) . ˙ W S includes all components of work, except that required for making the fluid flow into and out of the CV. ˙ W S may include, e.g. expansion work, stirrer work, electrical work, etc.. ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 8/18 Inlet and exit ‘plugs’ e t +∆ t t ˙ Q CV i ˙ W S t +∆ t t ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 9/18 Inlet and exit ‘plugs’ d e e e’ f f’ ˙ Q CV i c c’ ˙ W S b b’ a ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 10/18 A closed system • Occupies the space [abcdefa] at time t . • Occupies the space [ab’c’de’f’a] at time t + ∆ t . • No mass flows across the boundaries of this system during this period. • So this is a closed system. • We apply conservation of mass to this system. Then, the first law, and finally, the second law. ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 11/18 The system – intial state d e e e’ f f’ ˙ Q CV i c c’ ˙ W S b b’ a The system at time t ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 12/18 The system – final state d e e e’ f f’ ˙ Q CV i c c’ ˙ W S b b’ a The system at time t + ∆ t ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 13/18 Process and Interactions d e e e’ W e M ( t ) → M ( t +∆ T ) f f’ E ( t ) → E ( t +∆ T ) ˙ Q ∆ t V ( t ) → V ( t +∆ T ) S ( t ) → S ( t +∆ T ) i c c’ ˙ W S ∆ t W i b b’ a Process and interactions from t to t + ∆ t ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 14/18 Conservation of Mass M system ( t + ∆ t ) = M system ( t ) M system ( t ) = M CV ( t ) + M [bcc’b’] M system ( t + ∆ t ) = M CV ( t + ∆ t ) + M [eff’e’] M [bcc’b’] = ρ i A i V i ∆ t M [eff’e’] = ρ e A e V e ∆ t ∴ M CV ( t + ∆ t ) + ρ e A e V e ∆ t = M CV ( t ) + ρ i A i V i ∆ t M CV ( t + ∆ t ) − M CV ( t ) = ρ i A i V i − ρ e A e V e ∆ t So, in the limit as ∆ t → 0 , dM CV = ρ i A i V i − ρ e A e V e dt ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 15/18 Conservation of Mass (contd) We use the nomenclature: Rate of inflow of mass = ˙ m i = ρ i A i V i Rate of outflow of mass = ˙ m e = ρ e A e V e So we have: dM CV = ˙ m i − ˙ m e dt which is the basic form of conservation of mass. ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 16/18 First law - for the system ∆ E = Q − W But ∆ E = E system ( t + ∆ t ) − E system ( t ) E system ( t ) = E CV ( t ) + E [bcc’b’] E system ( t + ∆ t ) = E CV ( t + ∆ t ) + E [eff’e’] E [bcc’b’] = ( ρ i A i V i ∆ t ) e i E [eff’e’] = ( ρ e A e V e ∆ t ) e e ∴ ∆ E = E CV ( t + ∆ t ) + ( ρ e A e V e ∆ t ) e e − E CV ( t ) − ( ρ i A i V i ∆ t ) e i ∆ E = E CV ( t + ∆ t ) − E CV ( t ) + ˙ m e e e ∆ t − ˙ m i e i ∆ t We have: Q = ˙ Q ∆ t ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 17/18 First law - for the system (contd) W = ˙ W S ∆ t + W e + W i W e = p e A e V e ∆ t = p e v e ˙ m e ∆ t W i = − p i A i V i ∆ t = − p i v i ˙ m i ∆ t ∴ W e + W i = ˙ m e ( p e v e )∆ t − ˙ m i ( p i v i )∆ t ∴ the first law becomes E CV ( t + ∆ t ) − E CV ( t ) + ˙ m e e e ∆ t − ˙ m i e i ∆ t = ˙ Q ∆ t − ˙ W S ∆ t − ˙ m e ( p e v e )∆ t + ˙ m i ( p i v i )∆ t Transposing and combining terms: E CV ( t + ∆ t ) − E CV ( t ) = ˙ Q ∆ t − ˙ W S ∆ t + ˙ m i ( e i + p i v i )∆ t − ˙ m e ( e e + p e v e )∆ t ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde

Slide 18/18 First law - for the control volume dE CV = ˙ Q − ˙ W S dt + ˙ m i ( e i + p i v i ) − ˙ m e ( e e + p e v e ) We now expand e i + p i v i = u i + V 2 2 + gz i + p i v i = h i + V 2 2 + gz i i i e e + p e v e = u e + V 2 2 + gz e + p i v e = h e + V 2 2 + gz e e e Thus m i ( h i + V 2 m e ( h e + V 2 dE CV = ˙ Q − ˙ i e W S + ˙ 2 + gz i ) − ˙ 2 + gz e ) dt This is a reasonably general form of the first law for open systems. ME 209 THERMODYNAMICS Lecture 23 U. N. Gaitonde